Can you add geometry to a mesh over time (frames) with Python?
One way is to use the Sapling addon to create a tree. The addon needs to be enabled first in the User Preferences



After the settings were adjusted.

Convert it from curve to mesh Alt-C

Add a Build Modifier to the stem and another one to the leaves, you might want to add a few more loop cuts Ctrl-R to the stem so that the segments are displayed one by one.

To let the plant grow scale it down say 10% on frame 1, 50% on frame 10, 100% on frame 20
Set the Build modifiers start frame to 20 and 30.

Result:



.blend